(1) Field of Invention
The present invention relates to a system for measuring efficiency of communication or transportation through a network and, more particularly, to a system for measuring efficiency in a network using a measure that generalizes the network's average path length.
(2) Description of Related Art
Average path length (in the classical sense) is a general way to measure the efficiency of communication within a graph. Shorter average paths between vertices correspond to shorter distances or fewer intermediary steps for communication between one vertex and another. The usual measurement of average path length can become degenerate if several pairs of vertices are very distant from each other in a graph, though, when in fact the graph may be very efficient overall.
The classical notion of average path length is that all pairs of vertices are considered, their path lengths computed, and then averaged using the arithmetic mean. This has several disadvantages, as path lengths can be infinite, rendering the metric useless or inconvenient in some cases.
Thus, a continuing need exists for a metric that deals with infinite path length and optimizes a network to provide short average path length, producing networks which are more efficient.